WASHINGTON — Defiant and frustrated, President Barack Obama aggressively challenged Republicans today to get behind his jobs plan or explain why not, declaring that if Congress fails to act “the American people will run them out of town.”

The president used a White House news conference to attempt to heighten the pressure he’s sought to create on the GOP by traveling around the country, into swing states and onto the home turf of key Republican foes including House Speaker John Boehner and Texas Gov. Rick Perry.

Giving a bit of ground on his own plan, he endorsed a new proposal by Senate Democrats to tax millionaires to pay for his jobs program. “This is not a game,” he said.

Obama made no apologies for his decision to abandon seeking compromise with Republicans in favor of assailing them, sometimes by name. He contended that he’d gone out of his way to try to work with the GOP since becoming president, reaching hard-fought deals to raise the government’s borrowing limit and avert a government shutdown, and had gotten nothing in return.

“Each time, what we have seen is games playing,” the president said. “I am always open to negotiations. What is also true is they need to do something.”

Obama was still at the lectern when Senate Majority Leader Harry Reid told Republicans he would permit a test vote as early as late today on the president’s original measure. There was little doubt it would fail, the outcome Republicans hoped for.

The president predicted dire political consequences for his opponents if they don’t go along.

“I think the American people will run them out of town because they are frustrated and they know we need to do something big, something bold.”

“We will just keep on going at it and hammering away until something gets done,” he said. “And I would love nothing more than to see Congress act so aggressively that I can’t campaign against them as a do-nothing Congress.”

Yet Obama’s campaign has not swayed Capitol Hill Republicans who oppose the higher taxes he and other Democrats want to use to pay for his proposal. They accuse Obama of playing “campaigner in chief” instead of working with them.

“If the goal is to create jobs, then why are we even talking about tax hikes?” Senate Minority Leader Mitch McConnell, R-Ky., said today.

Republicans are resolutely opposed to much of Obama’s jobs initiative, both for its tax increases for wealthier people and small businesses and its reprise of stimulus spending on roads, bridges and schools and grants to local governments to pay the salaries of teachers and first responders. They criticize his bill as another version of his $825 billion stimulus of 2009, one that this time would rely on raising taxes.

Obama did say he would support a new approach by Senate Democrats for paying for his jobs bill with a tax on millionaires rather than his plan to raise taxes on couples making more than $250,000.

The president’s strident tone underscored a difficult political predicament as he seeks re-election with the economy slowing and unemployment stuck above 9 percent. “Our economy really needs a jolt right now,” he said.

The president said that without his nearly $450 billion package of tax cuts and public works spending there will be fewer jobs and weaker growth. He said the bill could guard against another economic downturn if the situation in debt-laden Europe worsens.

“If it turns out that there are Republicans who are opposed to this bill, they need to explain to me, but more importantly to their constituents — who’s the American people — why they’re opposed and what would they do.”

“What I’ve done over the last several weeks is to take the case to the American people so that they understand what’s at stake.”

Obama said the economy is weaker now than at the beginning of the year. Citing economists’ estimates, he said his $447 billion jobs bill would help the economy grow by 2 percent and create 1.9 million jobs.

“At a time when so many people are having such a hard time, we have to have an approach, we have to take action that is big enough to meet the moment,” he said.

Obama addressed the disaffection with politics pervasive among the public that’s driven down his approval ratings — and even more so, Congress’ — as he seeks a second term.

Appearing fed up, Obama blamed it on Republicans who he said refuse to cooperate with him even on issues where he said they once agreed with him. He talked about the ugly debate over raising the government’s borrowing limit that consumed Capitol Hill and the White House over the summer, until Obama gave in to Republican demands for deep spending cuts without new taxes.

“They don’t get a sense that folks in this town are looking out for their interests,” Obama said of Americans in general. “So if they see that over and over again, that cynicism is not going to be reduced until Congress actually proves their cynicism wrong by doing something.”

“What the American people saw is that the Congress didn’t care.”

Obama also said the “Occupy Wall Street” demonstrators protesting against Wall Street and economic inequality are expressing the frustrations of the American public.

He said he understands the public’s concerns about how the nation’s financial system works. And he said Americans see Wall Street as an example of the financial industry not always following the rules.

Asked why there hadn’t been more prosecutions in the financial sector, Obama said that many of the activities that precipitated the financial crisis in 2008 were not necessarily illegal. He said many financial schemes were probably immoral, inappropriate or reckless and required new regulations.

Obama criticized efforts in Congress, led by Republicans, to roll back some of the financial rules approved last year. He defended the Consumer Financial Protection Bureau created by that the legislation against GOP efforts to weaken it.

Obama also said that some banks are now using new regulations as an excuse to charge consumers more. It was a reference to a fee some banks are imposing to make up for restrictions on debit card fees they charge retailers.

“It’s not necessarily fair to consumers,” he said.

Obama also said the European Union has to act fast to deal with its debt crisis, but he said he is confident that European leaders are ready to take the necessary steps.

He said he hopes that European leaders have a “very clear, concrete plan of action that is sufficient to the task” by next month’s meeting of the Group of 20 rich and developing nations. Obama said the European debt crisis had already affected the U.S. economy.

On other topics, Obama:

—Said he was concerned by the Pakistani military and intelligence community’s ties to “unsavory characters.” But he said he is not inclined to cut off U.S. aid to Pakistan because he has a great desire to help the Pakistani people.

The president’s comments follow just-retired Joint Chiefs Chairman Adm. Mike Mullen’s claim that the Haqqani insurgent network acts as “a veritable arm” of Pakistan’s intelligence agency. While Obama did not endorse Mullen’s assertion, he did acknowledge that Pakistan engages with individuals the U.S. finds troubling. However, Obama said Pakistan has been a valuable partner in U.S. efforts to go after al-Qaida.

—Criticized China for “gaming” the trading system by keeping its currency undervalued but expressed concern that bipartisan Senate legislation to penalize China could conflict with international agreements. Still, he did not say whether he would veto the legislation.

—Defended his administration over two brewing controversies. One concerns a multimillion-dollar federal loan guarantee to a California solar company, Solyndra, that has declared bankruptcy and that Obama’s administration supported despite warnings over its solvency. The other involves a Justice Department program aimed at building cases against major weapons traffickers in Mexico that lost track of numerous guns.

On Solyndra, Obama said the loan guarantee program carried inherent risk, and the administration knew not every company would succeed. And he said continuing the program was crucial in order to counter China’s aggressive investments and subsidies to boost its own clean energy industry.

On the gun program, called Operation Fast and Furious, Obama said he has confidence in Attorney General Eric Holder, who’s come under criticism from Republicans. The president said both he and Holder would be “very unhappy” if guns were allowed to pass through to Mexico in a way that could have been prevented.